The max ammo carried by any ship for a specific weapon type is 70. Even if you have four missile launchers, you can only have 70 ammo for all of them if they're the same type of launcher.
Almost every ship in the game can use countermeasures - which have the same amount of 'ammo'. With a minimal amount of luck and skill, the target ship could easily run you out of ammunition and remain unharmed.
Further, while I was testing the liberty gunboat with 4 missile turrets in open singleplayer, it took an average of four to six volleys of missiles to destroy a nomad fighter, and more to destroy a BH hammerhead fighter. That's around 16-24 missiles used per target, which would leave the ship with no ammunition (and therefor zero ability to fight) after only 3-4 enemies.
Chances are, that ship would not be able to finish any missions for cash, and would end up unable to afford it's own ammo in a very short amount of time.
So please, no ammo requirements. I think they should take ammo requirements off of fighter missile launchers as well, maybe people would use them more often if that were the case.